Question: Solve for $x$ and $y$ using substitution. ${-6x+2y = -10}$ ${x = -y+11}$
Solution: Since $x$ has already been solved for, substitute $-y+11$ for $x$ in the first equation. ${-6}{(-y+11)}{+ 2y = -10}$ Simplify and solve for $y$ $6y-66 + 2y = -10$ $8y-66 = -10$ $8y-66{+66} = -10{+66}$ $8y = 56$ $\dfrac{8y}{{8}} = \dfrac{56}{{8}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {x = -y+11}\thinspace$ to find $x$ ${x = -}{(7)}{ + 11}$ $x = -7 + 11$ ${x = 4}$ You can also plug ${y = 7}$ into $\thinspace {-6x+2y = -10}\thinspace$ and get the same answer for $x$ : ${-6x + 2}{(7)}{= -10}$ ${x = 4}$